An accurate theory for the square-well potential: from long to short well width

Abstract

Density function theory (DFT) is combined with the first-order mean spherical approximation (FMSA) to study the radial distribution function (RDF) of the square-well (SW) potential. The combination (DFT + FMSA) is based on the direct correlation function (DCF) of the FMSA. Upon comparison with computer simulation data, DFT + FMSA is shown to give better performance than FMSA for mid- and long-range attractions. For short-range and very short-range attractions, the theory successfully corrects the deficiencies of the original FMSA. Comparisons include the evaluation of contact values, gap height at a discontinuity and profiles of the RDF. This work provides an accurate and consistent way to handle the SW potential.

Keywords:

• square-well potential
• first-order mean spherical approximation (FMSA)
• density function theory (DFT)
• radial distribution function (RDF)
• well width

Acknowledgement

The author thanks Dr J. Largo for sharing computer simulation data in all figures of this work.